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In chemistry, the equilibrium expression is a mathematical representation of the concentrations of reactants and products in a chemical equilibrium. For our specific case of the dissolution of \(\mathrm{Cd}(\mathrm{OH})_{2}\), the chemical equation is formulated as \(\mathrm{Cd}(\mathrm{OH})_{2}(s) \rightleftharpoons \mathrm{Cd}^{2+}(aq) + 2\mathrm{OH}^-(aq)\). Here, the substances are in equilibrium, which means there is a constant ratio of the products' concentrations to the reactants'.

The expression for the solubility product constant \(K_{sp}\) is derived by taking the concentrations of the ions formed. In our example:

• \([\mathrm{Cd}^{2+}]\) is the concentration of cadmium ions in equilibrium.
• \([\mathrm{OH}^-]^2\) is the squared concentration of hydroxide ions, since two hydroxide ions are produced for each cadmium ion.

The equilibrium expression for this reaction is: \(K_{sp}=[\mathrm{Cd}^{2+}][\mathrm{OH}^-]^{2}\). This helps us predict how many of the solid \(\mathrm{Cd}(\mathrm{OH})_{2}\) can dissolve in water until the system reaches equilibrium.

The solubility product constant, \(K_{sp}\), is a crucial concept in understanding solubility in chemistry. It provides insight into how soluble a compound will be in water. Specifically, \(K_{sp}\) is the product of the molar concentrations of the ions, each raised to the power of its coefficient in the balanced equation.

For \(\mathrm{Cd}(\mathrm{OH})_{2}\), the \(K_{sp}\) value is given as \(5.9 \times 10^{-15}\). This low \(K_{sp}\) value suggests that \(\mathrm{Cd}(\mathrm{OH})_{2}\) is not very soluble in water, as only a small amount will dissolve before reaching saturation and establishing equilibrium.

• \(K_{sp}\) is specific to temperature; the same substance may have different solubility at different temperatures.
• This constant allows chemists to predict the point at which a solution will become saturated and precipitation will begin.

Understanding \(K_{sp}\) helps in contexts like predicting mineral formation in natural waters or designing pharmaceuticals to ensure they dissolve properly in the body.

A reaction table is a simple yet effective tool used in chemistry to keep track of changes in concentrations of species as a reaction progresses towards equilibrium. It breaks down the stages from initial concentrations, through changes, to equilibrium concentrations. In our example of \(\mathrm{Cd}(\mathrm{OH})_{2}\), the reaction table helps us determine the extent to which the compound will dissolve.

The table is set up as follows:

• Initial concentrations: Start with zero concentrations of \(\mathrm{Cd}^{2+}\) and \(\mathrm{OH}^-\) because no reaction has occurred initially.
• Change (using variable \(s\)): The concentration of \(\mathrm{Cd}^{2+}\) increases by \(s\), and \(\mathrm{OH}^-\) increases by \(2s\) as each molecule of \(\mathrm{Cd}(\mathrm{OH})_{2}\) yields two hydroxide ions.
• Equilibrium concentrations: We use \(s\) and \(2s\) for \(\mathrm{Cd}^{2+}\) and \(\mathrm{OH}^-\) respectively, obtaining these by substituting back into the \(K_{sp}\) equation.

This systematic approach using a reaction table ensures clarity when solving equilibrium problems, helping us pinpoint how much of a substance can be expected to dissolve under given conditions.